What function represents a translation of the logarithmic function f(x) = log2 x that is 2 units to the right and 4 units up?

Question

f(x)=?

State it's domain:

1. all real numbers
2. x < 2    
3. x < 4
4. x > 2
5. x > 4

Select Range:

1. y < 2
2. y > 2    
3. all real numbers
4. y < 4
5. y > 4

Answer 1

2 units right is -2

4 units up is +4

f(x) = log₂(x-2)+4

Domain: x > 2 (normally the domain is x>0, 2 units shift to the right means x>2)

Range: all real numbers (regardless of shifts, the range is all real numbers